Some methods for finding error bounds for Newton-like methods under mild differentiability conditions
type: Item
instance of: scholarly article
title: Some methods for finding error bounds for Newton-like methods under mild differentiability conditions
zbMATH Open document ID: 0816.65033
DOI: 10.1007/BF01874679
author: Ioannis Konstantinos Argyros
published in: Acta Mathematica Hungarica
publication date: 1994-03-01T00:00:00Z
review text: The author extends convergence results of \textit{T. Yamamoto} [Numer. Math. 51, 545-557 (1987; Zbl 0633.65049)] for iterative methods of Newton-type applied to the solution of nonlinear equations \(F(x) = 0\) in Banach spaces. In particular, the Lipschitz condition for the derivative of \(F\) used by Yamamoto is replaced by a Hölder condition.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 508713
zbMATH Keywords: error bounds
zbMATH Keywords: Newton method
zbMATH Keywords: convergence
zbMATH Keywords: iterative methods
zbMATH Keywords: Banach spaces
zbMATH Keywords: Lipschitz condition
zbMATH Keywords: Hölder condition
reviewed by: Werner C. Rheinboldt
MaRDI profile type: Publication
cites work: On the approximate solutions of nonlinear functional equations under mild differentiability conditions
cites work: Q5563031
cites work: Q5577941
cites work: Q3967006
cites work: Q5332416
cites work: Majorizing Sequences and Error Bounds for Iterative Methods
cites work: A note on Newton type iterative methods
cites work: Sharp error bounds for Newton's process
cites work: A Unified Convergence Theory for a Class of Iterative Processes
cites work: Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
cites work: Untere Fehlerschranken für Regula-Falsi-Verfahren
cites work: A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
cites work: A convergence theorem for Newton-like methods in Banach spaces
description: scientific article; zbMATH DE number 508713